On new families of the Jacobsthal identities

Abstract

Formulas relating determinants to Jacobsthal numbers have been an object of recent interest. In some cases, these sequences arise as the determinant for certain families of matrices having integer entries, while in other cases these sequences are the actual entries of the matrix whose determinant is being evaluated. In this paper, we study some families of Toeplitz-Hessenberg determinants the entries of which are Jacobsthal numbers. The determinant formulas we have obtained may be rewritten as combinatorial identities involving sum of products of Jacobsthal numbers and multinomial coefficients.